In this investigation, I will attempt to find out some of the properties of a 2x2 square drawn within a 10x10 number grid. After this I hope to be able to investigate 9x9 and 8x8 grids, next I hope to move on to investigating rectangles.

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Daniel Lovegrove                        10CW

Maths Coursework

MATHS

Number Grid Coursework

Introduction

In this investigation, I will attempt to find out some of the properties of a 2x2 square drawn within a 10x10 number grid. After this I hope to be able to investigate 9x9 and 8x8 grids, next I hope to move on to investigating rectangles.

such as


when I find the product of the 2 sets of opposite corners I also find that the difference between these answers is ten:

My findings are laid out here algebraically (s= starting number)

The +10 in the lower left corner is there because every row has ten numbers and so if you look down the columns you will see that

here 35+10=40 and 36+10=46 and the

+1 is there obviously because every

number you count to the right is bigger

by 1 i.e. 35+1=36 I shall use the same method in all my working throughout this project

S(S+11) = S2 +11S

(S+10)(S+1) = S2 +10S +S + 10 = S2 + 11S + 10

The difference is ten

To find this I multiplied the corners of my square and found the difference between the products.

Next I investigated 3 x 3 squares within a 10 x 10 grid and found that the difference was 40

Again my results are laid out algebraically (s = starting number)

S(S+22) = S2 + 22S

(S+2)(S+20) = S2 + 20S + 2S + 40

The difference is 40

Now I will investigate 4 x 4 squares

Here are my results algebraically

S(S+33) =S2 + 33S

(S+30)(S+3) = S2 + 30S + 3S + 90 = S2 + 33S + 90

Difference = 90

I think I have spotted a pattern, but I will need one more set of results to know for sure so I will investigate 5 x 5 squares

I predict that the difference will be 160

Join now!

Here are my results algebraically

S(S+44) = S2 + 44S

(S+40)(S+4) = S2 + 44S + 160

The difference is 160 as I predicted

Squares                 Difference                      I noticed that the underlined

   2x2            (12)          10                            numbers were square numbers

   3x3            (22)          40             ...

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